Proves infinitely many periodic points for asymptotically linear non-degenerate Hamiltonian diffeomorphisms on R^{2n} that are unitary at infinity, decay quickly to their linear part, and obey a twist condition.
The Conley-Zehnder index for a path of symplectic matrices
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abstract
We give here a self contained and elementary introduction to the Conley-Zehnder index for a path of symplectic matrices. We start from the definition of the index as the degree of a map into the circle for a path starting at the identity and ending at a matrix for which 1 is not an eigenvalue. We prove some properties which characterize this index using normal forms for symplectic matrices obtained from geometrical considerations. We explore the relations to Robbin-Salamon index for paths of Lagrangians. We give an axiomatic characterization of the generalization of the Conley-Zehnder index for any continuous path of symplectic matrices defined by Robbin and Salamon.
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math.SG 1years
2024 1verdicts
UNVERDICTED 1representative citing papers
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A Poincar\'e-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms
Proves infinitely many periodic points for asymptotically linear non-degenerate Hamiltonian diffeomorphisms on R^{2n} that are unitary at infinity, decay quickly to their linear part, and obey a twist condition.